Puzzles and particularly integral, neatly packaged, multi-piece manipulable puzzles are popular for recreation and amusement. The interest for new and mentally challenging manipulable ("brainteaser") puzzles continues to grow, even in the face of the ubiquitous and increasingly sophisticated electronic amusement devices. "Brainteaser" inventions naturally augment recreation yet allow relaxed thoughtful self-improvement. A very popular form of manipulable puzzles is the portable and self-contained type which provides the user to define the desired level of activity and interruption without necessarily disrupting the user's progress. Also such puzzles foster collateral benefits such as promoting analytical thinking by requiring the user to predict the result of each particular manipulation as well as some enhancement of hand-eye coordination.